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( 7.050107 ")
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9 30.01.2005 .
곿 2005
658.012.2:336.714(07)
" ( 7.050107 ")/.: .., .. - 곿: , 2005. - 54 .
" , .
: . ..
. ..
: ..., . Ѻ ..
..., . ..
³ : . ..
1. -------------------------------------------------------------------------------------------4
2. ------------------------------------4
2.1. ----------------------------------------------------------------------------5
2.2. ------------------------------------------------------------------------5
2.3. -----------------------------------------------------------------------------------------6
2.4. -----------------------------------------------------------------------------6
2.5. ------------------------------------------------------------------------------------7
3. -----------------------------------------------------------------------------------------7
4. ˳---------------------------------------------------------------------------------------------------32
5. ------------------------------------------------------------------------------------------------------33
, .
- , " .
, .
- . ³ - , .
|
|
:
,
,
,
,
.
2.1. (NPV), () :
NPV = , (1)
t - ;
(t=,1,2,3,4,...)
Pt - () ;
d -
NPV - , ( ) , , .
:
NPT = - (2)
: tn - ,
tc - ,
KVt - ( ) t.
2.2. (IRR) , , IRR z :
, (3)
: = IRR - .
(1) .
2.3. , , , .
: - , , , .
(1), . ˳ , . h , .
г :
(4)
h ;
KV - .
2.4. (R), (profitability index) .
, (1) (R)
R= / (5)
, - .
2.5. () , . :
= (6)
: F - ;
;
V - .
3.1. - . , , , " ":
|
|
;
;
;
, .
- .
," | " | |
1. ' , , .. 2 , 3. , , . . . 1- 2- 3- 4- | 7100 2 10800 6300 4500 - - |
" 10%, " - 12% ( ' ).
1.
..." | ||||||
," | --------- | |||||
.. | 10% | .. | .. | 12% | .. | |
1- | 0,909 | 0,893 | ||||
1- | 0,826 | 0,797 | ||||
3- | - | - | - | 0,712 | ||
4- | - | - | - | 0,636 | ||
- | - |
, ".
1- -1: (1+0,1)=0,909
2- - 1:(1+0,1)^2=0,826
, ".
1- - 1: (1+0,12)=0,893
2- -1: (1+0,12) ^2=0,797
3- - 1: (1+0,12) ^3= 0,712
4- - 1: (1+0,12) ^4 = 0,636
2. ()
:
" 9444-7100-2344 ;
" 8615-6700=1915 .
, , " , ".
3. ():
"
9444: 7100 =1,33
"
8615: 6700 =1,29
" , " .
4. ().
4.1 :
- "
9444: 2 = 4722 ;
"
8615:4=2154 .
4.2. :
"
7100:4722=1,5 ;
"
6700:2154=3,11
" " ".
3.2. ϳ 100000 . . , , 6 ( ) 8000 . . 21000 .
³ (- , ), 16000 . . .
, 12% ? .
'
1. .
|
|
. . | |||
г | . . . . . | - 21000 8000 - | - 100000 16000 - |
2 :
:
. | , . | |||
1-6 | -100000 21000 8000 | 1,000 4,12 0,507 | -100000 86352 4056 | |
-9592 |
:
0- = 1
1-6-
+ + + + + = 0,893 + 0,797 + 0,712 + 0,636 + 0,567 + 0,507 = 4,112
6- = 0,507
, . | , . | |||
1-6 | -100000 | 4,12 0,507 | -100000 | |
3. :
- ;
- ' .
3.3. 12. .
() :
1- | 2- | 3- | 4- | |
. . | 4,0 | 6,0 | 8,0 | 3,0 |
() 10%, 20% 30% ().
'
.
, 10% | , | , 20% | , . | , 30% | , . | |
1- | 0,909 | 0,833 | 0,769 | 3,76000 | ||
2- | 0,826 | 0,694 | 0,592 | |||
3- | 0,751 | 0,579 | 0,455 | |||
4- | 0,683 | 0,482 | 0,350 | |||
- | - | - | ||||
-682000 |
10%:
1- = 0,909; 2- = 0,826;
3- = 0,751; 4- = 0,683;
20%:
1- = 0,833; 2- = 0,694;
3- = 0,579; 4- = 0,482;
30%:
1- = 0,769; 2- = 0,592;
3- = 0,455; 4- = 0,350;
.
30% . , 20 30%.
.
-682000
, :
= + ,
- ; - ;
-, - ;
- ;
- , .
= 20% + = 26,98%.
3.4. () (), ( ):
1 = 10.., 2 = 200.., 3 = 400.., 4 = 480..,
|
|
: R1 = 0, R2=640.., R3 = 1440.., R4 = 480..;
- 100% =1,0.
'
(3) (R) . .
1. :
=
, t - t;
- ;
t- (1=1...).
= + = 80+50+50+30=210 ..
2.
RT =
, Rt - t.
Rt = + = 0+160+180+95 = 435.
3. :
= Rt - = 435 - 210 = 225..
- :
= RT / T = = 2,07.
: , - , .
3.5. , () :
1- | 2- | 3- | 4- | 5- | |
. . | -25,0 | -15,0 | -5,0 | 30,0 | 40,0 |
1 = 15%, 2 = 17%, , , .
'
1. 1 = 15% :
1- - 0,870; 2- - 0,756; 3- - 0,658; 4- - 0,572; 5- - 0,497
2=17% 1- -0,855; 2- -0,731; 3- -0,634; 4- -0,534; 5- -0,456.
2. 2, =0,15% :
(-25,0*0,870)+(-15*0,756)+(-5*0,658)+(30*0,572)+(40*0,497)= -36,38+37,04=0,660;
2 =0,17% :
(-25*0;855)+(-15*0,731)+(-5*0,624)+(30*0,534)+(40*0,456)= -35,46+34,26=-1,20.
, , = 15% 2 =17%.
3. , :
= 1 + [3 *(2 - 1) / 3 + 3]
, -
3- 1;
3 - 2;
3 3 .
= 15 + [0,660* (17 -15)/(0,660 + 1,20)]= 15 + 0,71 = 15,71%
4. .
4.1. = 15,71% :
1- = 0,86423; 2- = 0,74689;
3- = 0,74689; 4- = 0,55785;
5- = 0,48211
4.2. = 15,7% :
(-25*0,86423)+(-15*0,74689)+(-5*0,64549)+(0*0,55785)+(40*0,48211)=21,6-11,2-3,2+16,7+19,3=-36,0+36,0=0
3.6. ϳ 2- : 120000 . 70000 . - . 8 ' , 62000 . . 30; 50; 70; 90% . ϳ , , 16% . :
- ;
- .
'
1 .
- 62000*0,3=18600 .;
- 62000x0,5=31000 .;
- 62000x0,7=43400 .;
- 62000x0,9=55800 .;
, - 62000 ..
2. 1
1.
. | , . | |||
(120000) | 1,0 | (120000) | ||
(70000) | 0,8621 | (60347) | ||
0,8621 | ||||
0,7432 | ||||
0,6407 | ||||
0,5523 | ||||
0,4761 | ||||
0,4104 | ||||
0,3538 | ||||
0,3050 | ||||
3. .
|
|
. : (60347)+16035=(44312) . . .
4. 2
:
2.
г | , . | |
(120000) (44312) | (120000) (164312) (141273) (113466) (82648) (53130) (27685) (5749) |
, . :
8 = 7 + = 7,3 .
3.7. ϳ , 8 , , :
130000 . - ;
25000 . - ;
20000 . - ;
15000 . - ' ;
10000 . - .
, , 25000 . 35000 . .
( ) :
1- | 2- | 3- | 4- | 5- | 6- | 7- | 8- | |
. |
12%- .
'
:
, . | , . | |||
-130000 | 1,0 | -130000 | ||
-25000 | 0,893 | -22325 | ||
0,893 | ||||
-20000 | 0,797 | -15940 | ||
0,797 0,712 0,636 | ||||
-15000 | 0,636 | -9540 | ||
0,567 | ||||
-10000 | 0,507 | -5070 | ||
0,507 0,452 0,404 | ||||
0,404 | ||||
0,404 | ||||
:
0- = 1; 1- = 0,893; 2- = 0,797;
3- = 0,712; 4- = 0,636; 5- = 0,567;
6- =0,507; 7- =0,452; 8- = 0,404.
, .
: , .
3.8. . , , :
г | . . | . .. |
-10 | -_ | |
-800 | -_ | |
-400 | ||
-200 | ||
-100 | ||
-100 |
, 10% .
, 18%? , - .
'
10% 18%, 1.
10%:
1- = 0,909; 2- = 0,826; 3- = 0,751;
4- = 0,683; 5- = 0,621
1.
, ..
г | , | , | 10% | - | 10% | 10% | 10% | 10% | 18% |
-10 | - | - | -10 | -10 | - | -10 | - | -10 | |
-800 | - | 0,909 | -800 | -727,2 | - | -727,2 | 0,847 | -677,6 | |
-400 | 0,826 | -300 | -247,8 | 82,6 | -330,4 | 0,718 | -215,4 | ||
-200 | 0,751 | 225,3 | -150,2 | 0,609 | 60,9 | ||||
-100 | 0,683 | 341,5 | 409,8 | -68,3 | 0,516 | 258,0 | |||
-100 | 0,621 | 683,1 | 745,2 | -62,1 | 0,437 | 480,7 | |||
∑ | -1610 | 114,7 | 1462,9 | -1348,2 | -103,4 |
18%:
1- = 0,847; 2- = 0,718; 3- = 0,609;
4- = 0,516; 5- = 0,437
10% NPV 114,7 . ., - B: = = 1,085, , NPV >0, :>1.
18% , NPV 18% = -103,4 . .., :18% = 0,87 < 1, .
, , .
IRR = 10+
, 10% , 14,2 % . , 18% .
. 3.1 - 3.8 1-8.
3.9. ϳ , , 18% . 84500 . Ҳ. , , 17000 . 15 .
, , 2500 . .
3.10 Գ , 150 . . -60 ., -7200 . .
3.11. 18000 . ; : -1500 . , 8 - 3600 . .
, 10%.
3.12. 1. , 10 %.
2. .
г | , . | (. .), . . | |
0,00 | 1,09 | 0,00 | |
0,00 | 4,83 | 0,00 | |
0,00 | 5,68 | 0,00 | |
0,00 | 4,50 | 0,00 | |
0,00 | 1,99 | 0,00 | |
1,67 | 0,00 | 0,67 | |
3,34 | 0,00 | 0,97 | |
5,00 | 0,00 | 1,30 | |
6,68 | 0,00 | 1,62 | |
10-30* | 8,38 | 0,00 | 2,95 |
* 3 , 10- 30-
3.13. , . .
? 0,2. ?
1 | 2 | 3 | |
3.14. X. .
, 10 . .
.
, | 2,0 | 2,5 | ||
1,0 | 0,8 | |||
3,0 | 2,5 | |||
0,7 | 0,5 | |||
0,5 | 0,4 | |||
1,0 | 0,8 | |||
: | 8,2 | 7,5 |
3.15. Գ X . 100 . . , , 50 . . , 8 25 . . , 10 , , , , 80 . .
, , ?
3.16. 600 . . 8 150 .. . .
3.17. , , , :
1- - 50 . .; 2- - 100 . .; 3- - 200 . .; 4- - 250 . .; 5- - 300 . . .
3.18. 2 . . 1 . . ( ) 10%?
3.19. 1 . ., 10 . , , , 20 . .( ).
40%.
, , 10 .
(ROI).
3.20. 360 . . . , 100 . . 5 , ( ).
(') 10%, - 18%, , .
20 . . ( ).
?
3.21. , - - .
10%. 5 , 100 . .
7 120 . .
?
3.22. , 100 . . 3- , - 4- - ' . , ( ) 100 . . 5 .
10% . ' .
3.23. ̳ ' , . 0. 1 3 .
, 5 . ., - 30 . .; 2, 3 4 - 10,15 20 . ., ( ) - 10%.
3.24. ϳ 40 . . 35,60, 80 100 . .
. г 100%.
3.25. 200. . , 10 , 140 . . 10- 300 . . 13% .
.
3.26. 600 . . , 10 , 1300 . . 10- 900 . . 13% .
.
3.27. Գ . 75% . 40 .. 15 . . 6 .
.
3.28. 12 . . :
1 - 4 . ;
2 - 6 . ;
3 - 8 . ;
4 - 3 . .
.
3.29. , 2 . 5000 . , 1000 . 10 . 10%.
?
3.30. 15%. Գ :
(.) | |
-27000000 | |
+12000000 | |
+11520000 | |
?
3.31. , 10%. - :
, . | |||
-5000 | -10000 | 1,00 | |
-20000 | 0,50 |
?
3.32. , , , , 25% . , - 10%? :
0 | 1 | 2 | 3 |
-1000000 | +250000 | +250000 | - |
3.33. , - 200000 . ?
3.34. , - 200000 . Գ , , 10%.
?
3.35. 16000 . 100 . 3000 , 7000 . 6 , 3000 ( ). 12% .
.
3.36. 䳺 . :
1. 40000 58000 3 . 2. 40000 46000 .
4 .
- 10%.
3.37. , 16% RRR:
: 30000 , 15000 6 .
: 20000 , 18000 3 .
.
3.38. 20000 7000 6 .
, 15%.
3.39. , $ 160000, $30000 15 . , 15%.
3.40. , 15 , $150 000. ' , 10 $50 000. , 15%?
3.41. , $:
1 2
-4000 2500 3000
-2000 1200 1500
IRR, NPV, r =10%.
3.42. NPV IRR, 20 %.
-370 - - - - 1000
-240 60 60 60 60 -
-263,5 100 100 100 100 100
3.43. , 10%:
-100 120 - - -
-100 - - - 174
3.44. NPV, IRR , 13 %:
-20000 7000 7000 7000 7000
-25000 2500 5000 10000 20000
˳,
1. : . . . .- .: "-",1995. - 240.
2 .. . - .:" -", 1997. 144 .
3 .., ., .. . - .: - "", 1997. - 272 .
4 .., .. - . - .: - "", 1998. - 208 .
5 .. : . . - .: "", 1998 - 463 .
6 .., ., ij .. . . - : " ˳", 1998. - 386 .
7 .., .. : . - .: , , 1998. -423 .
8 .. , .. , ... . - . - : - , ,1999.-304 .
9 .., .. ; ϳ.- .: ,2000.-322.
10 .. : / . . . .. .-.: , 2001.- 400.
11. .. . - .: - "- 97",2001.-208.
12. .. : . .- .: , 2002.-200:.-.: . 193-196.